Answer:
The value of x is 16 and the value of y is 8.
Step-by-step explanation:
Consider the provided equation.
[tex]\frac{3}{4}x -\frac{1}{2}y= 8\ and\ 2x +y=40[/tex]
Isolate x for [tex]\:\frac{3}{4}x-\frac{1}{2}y=8[/tex]
[tex]\frac{3}{4}x-\frac{1}{2}y+\frac{1}{2}y=8+\frac{1}{2}y[/tex]
[tex]\frac{3}{4}x=8+\frac{1}{2}y[/tex]
Multiply both side by 4 and simplify.
[tex]3x=32+2y[/tex]
[tex]x=\frac{32+2y}{3}[/tex]
Substitute the value of x in [tex]2x +y=40[/tex]
[tex]2\cdot \frac{32+2y}{3}+y=40[/tex]
[tex]\frac{64}{3}+\frac{7y}{3}=40[/tex]
[tex]64+7y=120[/tex]
[tex]7y=56[/tex]
[tex]y=8[/tex]
Now substitute the value of y in [tex]x=\frac{32+2y}{3}[/tex]
[tex]x=\frac{32+2\cdot \:8}{3}[/tex]
[tex]x=16[/tex]
Hence, the value of x is 16 and the value of y is 8.
